3abc

Multiply: 2/3 abc (a^2+b^2-3c^2)

Let 5log_(abc) (a^3+b^3+c^3)=3lambda((1+log_3 (abc))/(log_3 (abc))) and (abc)^(a+b+c)=1 and lambda=m/n m, n are relatively prime , find |m+n|+|m-n|

Let 5log_(abc)(a^(3)+b^(3)+c^(3))=3 lambda((1+log_(3)(abc))/(log_(3)(abc))) and (abc)^(a+b+c)=1 and lambda=(m)/(n)m,n are relatively prime,find |m+n|+|m-n|

Let 5log_(abc) (a^3+b^3+c^3)=3lambda((1+log_3 (abc))/(log_3 (abc))) and (abc)^(a+b+c)=1 and lambda=m/n m, n are relatively prime , find |m+n|+|m-n|

Let 5log_(abc) (a^3+b^3+c^3)=3lambda((1+log_3 (abc))/(log_3 (abc))) and (abc)^(a+b+c)=1 and lambda=m/n m, n are relatively prime , find |m+n|+|m-n|

If p_(1),p_(2),p_(3) are altitudes of a DeltaABC then show that P_(1)P_(2)P_(3)=((abc)^(2))/(8R^(3))=(8Delta^(3))/(abc)

If P_(1),P_(2),P_(3) are altitudes of a DeltaABC then show that P_(1)P_(2)P_(3)=((abc)^(2))/(8R^(3))=(8Delta^(3))/(abc)

Prove that : |{:(a+b,b,c),(b+c,c,a),(c+a,a,b):}|=3 abc-a^(3)-b^(3)-c^(3)